Incenter of a Triangle

In this activity, you will explore the incenter of a triangle. Each angle of the triangle below has an angle bisector. Drag points A, B, and C to uncover patterns about the angle bisectors of different types of triangles.

What do you notice about the intersection of the angle bisectors? Is this always true? Drag the vertices of the triangle to see what happens to the intersection as the triangle changes.

All three angle bisectors will always intersect at the same point. This point is called the incenter.

The applet above contains the same triangle with angle bisectors as the first applet. The incenter is labelled point D. Then, we drew a circle centered at D that touches side BC of the triangle. What do you notice about the other sides of the triangle?

Write a 1-3 sentence summary of what you learned about the incenter of a triangle.